Statics and mechanics of materials: an integrated approach

735 Pages·2002·22.267 MB·English

by  Riley, William Franklin;Sturges, Leroy D.;Morris, Don H

S M
TATICS AND ECHANICS
M :
OF ATERIALS
A I
N NTEGRATED
A
PPROACH
Second Edition
William F. Riley
Distinguished Professor Emeritus
Iowa State University
Leroy D. Sturges
Aerospace Engineering and Engineering Mechanics
Iowa State University
Don H. Morris
Engineering Science and Mechanics
Virginia Polytechnic Institute and State University
JOHN WILEY & SONS, INC.
William F. Riley
1925–2000
Friend, Colleague, Mentor
ACQUISITIONS EDITOR Joseph Hayton
MARKETING MANAGER Katherine Hepburn
DESIGNER Dawn L. Stanley
This book is printed on acid-free paper.(cid:2)∞
Copyright 2002© John Wiley & Sons, Inc. All rights reserved.
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Library of Congress Cataloging-in-Publication Data
Sturges, Leroy D.
Statics and mechanics of materials : an integrated approach / Leroy D. Sturges, Don H.
Morris.—2nd ed.
p. cm.
Rev. ed. of: Statics and mechanics of materials / William F. Riley, Leroy D. Sturges,
Don H. Morris. c1995.
ISBN 0-471-43446-9
1. Strength of materials. 2. Statics. I. Morris, Don H., 1939- II. Riley, William F.
(William Franklin), 1925- Statics and mechanics of materials. III. Title.
TA405.R56 2001
620.1'12--dc21
2001046630
95–4072
CIP
Printed in the United States of America
10 9 8 7 6 5
P
REFACE
APPROACH/PHILOSOPHY
The purpose of courses in engineering mechanics is to describe the effects that forces have on bodies and struc-
tures. The traditional introduction to mechanics consists of a course in statics followed by a course in mechanics
of materials. The principles of statics are used to determine the forces that act on or in a structure, assuming that
the structure is perfectly rigid and does not deform. Then, these forces, along with the theory developed in me-
chanics of materials, are used to determine how the material deforms or reacts.
This book approaches the teaching of mechanics using the just-in-time approach. As soon as the student
has studied equilibrium of concurrent force systems, he or she is ready to calculate stretches of wires and rods
using a one-dimensional Hooke’s law. After studying rigid body equilibrium, the student is ready to calculate
stresses and deformation in members such as shafts and beams. When the two subjects are integrated in a uni-
fied course in this manner, students can immediately see the use of the principles of statics; they can see the in-
terrelationship of statics and mechanics of materials.
Free-Body Diagrams. We strongly feel that a proper free-body diagram is very important in all mechanics
courses. It is our approach that, whenever an equation of equilibrium is written, it must be accompanied by a
complete, proper free-body diagram. Furthermore, since the primary purpose of a free-body diagram is to show
the forces acting on a body, the free-body diagram should not be used for any other purpose. We encourage stu-
dents to draw separate diagrams to show deformation and compatibility relationships.
Problem-Solving Procedure. Students are urged to develop the ability to reduce problems to a series of
simpler component problems that can be easily analyzed and combined to give the solution of the initial prob-
lem. Along with an effective methodology for problem decomposition and solution, the ability to present results
in a clear, logical, and neat manner is emphasized throughout the text.
Homework Problems. The illustrative examples and homework problems have been selected with special
attention devoted to problems that require an understanding of the principles of mechanics of materials without
demanding excessive time for computational work. Over 1100 homework problems are included so that problem
assignments may be varied from term to term. The problems in each set represent a considerable range of diffi-
culty and are grouped according to this range of difficulty. Mastery, in general, is not achieved by solving a large
number of simple but similar problems. While the solution of simple problems is necessary to build a student’s
problem-solving skills and confidence, we believe that a student gains mastery of a subject through application
of basic theory to the solution of problems that appear somewhat difficult.
SI versus U.S. Customary Units. U.S. customary units and SI units are used in approximately equal pro-
portions in the text for both example problems and homework problems. To help the instructor who wants to
iv PREFACE
assign problems of one type or the other, odd-numbered homework problems are in U.S. customary units and
even-numbered homework problems are in SI units.
Answers Provided. Answers to about half of the homework problems are included at the end of this book.
Since the convenient designation of problems for which answers are provided is of great value to those who make
up assignment sheets, the problems for which answers are provided are indicated by means of an asterisk (*)
after the problem number.
Emphasis on Fundamentals. This book is designed to emphasize the required fundamental principles,
with numerous applications to demonstrate and develop logical, orderly methods of procedure. Instead of deriv-
ing numerous formulas for all types of problems, we have stressed the use of free-body diagrams and the equa-
tions of equilibrium, together with the geometry of the deformed body and the observed relations between stress
and strain, for the analysis of the force system acting on a body.
Emphasis on Clarity. The emphasis is always on keeping the material understandable to the student. Clar-
ity is never sacrificed for the sake of mathematical elegance. Calculus and vector methods are used where nec-
essary and where appropriate. However, if scalar methods are more appropriate and/or are commonly used by
practicing engineers, then these methods are generally used in the example problems.
NEW TO THIS EDITION
In addition to new and revised homework problems, this edition has 27 new example problems including 6 new
computational example problems. The review of vector operations, which was previously in an appendix, has been
integrated into the appropriate sections of Chapters 2 and 5. The structural applications in Chapter 6 have been
rearranged so that the discussion of frames and machines precedes the discussion of trusses. A common mistake
that students make when they see trusses before frames is to draw forces along the axis of structural members
that are not two-force members. This new arrangement should help students recognize that forces in structures
often do not act along the axis of the structural members. Design of ductile and brittle materials (including the-
ories of failure) has been added to Chapter 10, and eccentrically loaded columns have been added to Chapter 11.
In addition, several minor sections in Chapters 4 through 9 have been promoted to major sections for better or-
ganization of the material.
ORGANIZATION
After a brief introduction to mechanics in Chapter 1, Chapter 2 describes the characteristics of forces and devel-
ops the mathematics necessary to work with concurrent forces. These concepts are immediately used in Chapter
3 to calculate the forces acting on a particle in equilibrium. The basic discussion is completed in Chapter 4, where
stress, strain, and the relationship between loads and deformation is presented. Chapter 5 continues the descrip-
tion of forces, develops the concept of equivalent force-couple systems, and explores the effects of forces and
couples on rigid bodies. Chapter 6 presents the equilibrium of rigid bodies and its use in several structural ap-
plications. The final five chapters consist of standard topics of Mechanics of Materials—torsion of circular shafts
(Chapter 7), flexural stresses in beams (Chapter 8), deflections of beams (Chapter 9), combined loadings (Chap-
ter 10), and columns and other compressive members (Chapter 11). Second moments of areas are introduced and
developed where needed in Chapters 7 and 8.
PEDAGOGY
Every chapter opens with a brief introduction and ends with a summary of important concepts covered in the
chapter, followed by a set of review problems. All principles are illustrated by one or more example problems and
several homework problems. The homework problems are graded in difficulty and are separated into groups of
PREFACE v
introductory, intermediate, and challenging problems. Several sections include a set of computer problems that
require students to analyze how the solution depends on some parameter of the problem. While the computations
could be accomplished by the student writing a FORTRAN program, the computations could just as easily be car-
ried out using MathCAD, Mathematica, or a spreadsheet program. The important concept of the computer prob-
lems is that they require students to analyze how the solution depends on some parameter of the problem.
Design. Most chapters conclude with a section on design that includes example problems and a set of home-
work problems. The emphasis in these problems is that there is often more than just one criterion to be satisfied
in a design specification. An acceptable design must satisfy all specified criteria. In addition, standard lumber,
pipes, beams, and so on come in specific sizes. The student must choose an appropriate structural member from
these standard materials. Since each different choice of a beam or a piece of lumber has a different specific weight
and affects the overall problem differently, students are also introduced to the idea that design is an iterative
process.
ACKNOWLEDGMENTS
We are grateful for comments and suggestions received from colleagues and from users of the earlier edition of
this book. We would like to particularly mention those people who provided feedback on revision plans and parts
or all of the new edition. They include Jim Elkins, Oklahoma Christian University; Hamid Garmestani, FAMU-
FSU; David S. Hansen, United States Air Force Academy; Takeru Igusa, Johns Hopkins University; Thomas
Juliano, New Jersey Institute of Technology; Richard D. Keane, University of Illinois; John S. Klegka, United
States Military Academy; Nels Madsen, Auburn University; K.T. Ramesh, Johns Hopkins University; Risa J.
Robinson, Rochester Institute of Technology; and Douglas J. Wendel, Snow College. Final judgments concerning
organization of material and emphasis of topics, however, were made by the authors. Finally, we thank our
families for their constant support of our efforts.
E-mail address. We will be pleased to receive comments from readers and will attempt to acknowledge all
such communications. Comments can be sent by e-mail to [email protected] or to [email protected].
C
ONTENTS
PREFACE 2-3 Resultant of Two or More Concurrent Forces 29
Addition of Vectors 29
Law of Sines and Law of Cosines 30
CHAPTER 1: GENERAL PRINCIPLES
Resultant of Two Concurrent Forces 30
1-1 Introduction 1 Resultant of Three or More Concurrent Forces 31
1-2 Fundamental Quantities of Mechanics 2 2-4 Resolution of a Force into Components 38
Newton’s Laws 3
2-5 Rectangular Components of a Force 43
Mass and Weight 5
Unit Vectors 44
1-3 Units of Measurement 8 Rectangular Components in Two Dimensions 44
The U.S. Customary System of Units 9 Rectangular Components in Three Dimensions 45
The International System of Units 9 The Scalar (Dot) Product and Rectangular
Components 46
1-4 Dimensional Considerations 13
Dimensional Homogeneity 13 2-6 Resultants by Rectangular Components 53
1-5 Method of Problem Solving 16 2-7 Summary 62
1-6 Significance of Numerical Results 18
The Accuracy of the Known Physical Data 18 CHAPTER 3: EQUILIBRIUM: CONCURRENT
The Accuracy of the Physical Model 19 FORCE SYSTEMS
The Accuracy of the Computations Performed 19
3-1 Introduction 65
1-7 Summary 23
3-2 Free-Body Diagrams 66
CHAPTER 2: CONCURRENT FORCE SYSTEMS
3-3 Equilibrium of a Particle 68
Two-Dimensional Problems 69
2-1 Introduction 26
Three-Dimensional Problems 69
2-2 Forces and Their Characteristics 26
3-4 Summary 84
Scalar Quantities 27
Vector Quantities 27
Principle of Transmissibility 28 CHAPTER 4: STRESS, STRAIN, AND
Classification of Forces 28 DEFORMATION: AXIAL LOADING
CONTENTS vii
4-1 Introduction 88 5-8 Centroids of Volumes,Areas,and Lines 205
Centroids of Volumes 205
4-2 Axially Loaded Members—Internal Forces 88
Centroids of Areas 206
Normal Stress Under Axial Loading 89
Centroids of Lines 206
Shearing Stress in Connections 90
Centroid, Center of Mass, or Center of Gravity by
Bearing Stress 92
Integration 206
4-3 Stresses on an Inclined Plane in an Axially Loaded
5-9 Centroids of Composite Bodies 214
Member 103
5-10 Distributed Loads on Structural Members 225
4-4 Displacement,Deformation,and Strain 108
5-11 Summary 231
4-5 Stress–Strain–Temperature Relationships 114
Stress–Strain Diagrams 114
CHAPTER 6: EQUILIBRIUM: RIGID AND
4-6 Thermal Strain 125 DEFORMABLE BODIES
4-7 Deformation of Axially Loaded Members 127 6-1 Introduction 237
4-8 Statically Indeterminate Axially Loaded 6-2 Free-Body Diagrams 238
Members 133 Idealization of Two-Dimensional Supports and
Connections 239
4-9 Thermal Effects 140 Idealization of Three-Dimensional Supports and
Connections 242
4-10 Design 146
6-3 Equilibrium in Two Dimensions 248
4-11 Summary 152
Two-Force Members 249
Statically Indeterminate Reactions and Partial
CHAPTER 5: EQUIVALENT FORCE/ Constraints 251
MOMENT SYSTEMS
6-4 Frames and Machines 275
5-1 Introduction 158 Frames 276
Machines 278
5-2 Moments and Their Characteristics 158
Stress and Deformation: Frames and Machines 279
Principle of Moments—Varignon’s Theorem 159
6-5 Statically Indeterminate Problems 290
5-3 Vector Representation of a Moment 164
6-6 Plane Trusses 299
Moment of a Force About a Point 167
Method of Joints 302
5-4 Moment of a Force About a Line (Axis) 175 Zero-Force Members 303
Method of Sections 305
5-5 Couples 182
6-7 Equilibrium in Three Dimensions 319
5-6 Equivalent Force-Couple Systems 187
Coplanar Force Systems 188 6-8 Friction 325
Noncoplanar Parallel Force Systems 189 Characteristics of Coulomb Friction 325
General Force Systems 190
6-9 Flat Belts and V-Belts 339
5-7 Center of Gravity and Center of Mass 201
6-10 Design 346
Center of Gravity 201
Center of Mass 202 6-11 Summary 350
viii CONTENTS
8-9 Design 475
CHAPTER 7: TORSIONAL LOADING: SHAFTS
8-10 Summary 481
7-1 Introduction 357
CHAPTER 9: FLEXURAL LOADING:
7-2 Torsional Shearing Strain 359
BEAM DEFLECTIONS
7-3 Torsional Shearing Stress—The Elastic Torsion
Formula 361 9-1 Introduction 487
7-4 Torsional Displacements 362 9-2 The Differential Equation of the Elastic Curve 487
7-5 Stresses on Oblique Planes 376 9-3 Deflections by Integration 489
7-6 Work of Forces and Couples 381 9-4 Deflections by Integration of Shear-Force or Load
Work of a Force 381 Equations 502
Work of a Couple 383
9-5 Singularity Functions 506
7-7 Power Transmission by Torsional Shafts 387
9-6 Deflections by Superposition 517
7-8 Statically Indeterminate Members 391
9-7 Statically Indeterminate Beams: The Integration Method
7-9 Design 400 525
9-8 Statically Indeterminate Beams:The Superposition
7-10 Summary 406
Method 534
9-9 Design 540
CHAPTER 8: FLEXURAL LOADING:
STRESSES IN BEAMS 9-10 Summary 547
8-1 Introduction 410
CHAPTER 10: COMBINED STATIC LOADING
8-2 Flexural Strains 413
10-1 Introduction 551
8-3 Flexural Stresses 414
10-2 Stress at a General Point in an Arbitrarily Loaded
8-4 Second Moments of Areas 417 Member 551
Radius of Gyration 417
10-3 Two-Dimensional or Plane Stress 554
Parallel-Axis Theorem for Second Moments of
Area 417 10-4 The Stress Transformation Equations for Plane Stress 558
Second Moments of Composite Areas 418
10-5 Principal Stresses and Maximum Shearing
8-5 The Elastic Flexure Formula 426 Stress—Plane Stress 564
8-6 Shear Forces and Bending Moments in Beams 435 10-6 Mohr’s Circle for Plane Stress 575
Shear Force and Bending Moment: An Equilibrium
10-7 Two-Dimensional or Plane Strain 585
Approach 436
10-8 The Strain Transformation Equations for Plane Strain 586
8-7 Load,Shear Force,and Bending Moment
Relationships 446 10-9 Principal Strains and Maximum
Shear Force and Bending Moment Diagrams 449 Shearing Strain 591
8-8 Shearing Stresses in Beams 461 10-10 Mohr’s Circle for Plane Strain 593